The present invention relates to radial piston machines in general and more particularly to improvements in radial piston machines wherein the pistons reciprocate in discrete cylinders each of which abuts against a stationary sealing surface, especially a convex or spherical surface. Such types of radial piston machines are often employed as slowly running hydraulic motors with a high torque transmission. As a rule, the heads or shoes of the pistons directly engage the device which causes the pistons to reciprocate in the respective cylinders; therefore, the pressure upon the pistons must be reduced as much as possible in order to avoid a reduction in efficiency due to frictional losses and/or due to wear upon the shoes and/or the reciprocating device. When a machine of the just outlined character is used as a radial piston motor and the means for reciprocating the pistons comprises a crankshaft having an eccentric portion in the form of a crank pin, the flow of hydraulic fluid into the cylinder chambers is regulated by a rotary spool valve which is coupled to the crankshaft. Such mode of regulating the inflow of fluid is not satisfactory when the machine is used as a pump because the quantity of fluid which enters the cylinder chambers by suction is practically nil. Therefore, all radial piston machines of the above outlined character which are used as pumps employ valves wherein the valve members are biased against seats, and such valves are immediately or closely adjacent to the outer ends of cylinders. The just described mounting of the valves contributes to a reduction of dead space.